Filter that minimizes in-band noise and maximizes detection sensitivity of exponentially-modulated signals

ABSTRACT

The trans-filter compresses in band AWGN, demodulates input signals and has no threshold due to applied noise. Two frequency selective networks with opposite amplitude vs frequency slopes are designed to remain 180 degrees out of phase over the signal band. Output amplitudes are equal at band center and are summed producing a monotonic amplitude vs frequency characteristic going thru zero at center frequency with abrupt phase reversal. This produces the parabolic output noise density and differentiates applied signals. Absence of nonlinear circuit components and product devices prevents generation of noise×noise products, avoiding the threshold phenomenon. Exponentially modulated digital signals produce output impulses due to the slope and abrupt phase reversal. The impulses have strong fundamental frequency components and may be recovered at baseband without frequency conversion. Cascading trans-filters increases noise reduction and impulse amplitude. The trans-filter algorithm may be used separately or in conjunction with one or more hardware trans-filters.

CROSS-REFERENCE TO RELATED APPLICATIONS

This U.S. national phase application claims the benefit under 35 U.S.C.§ 371 of PCT Application No. PCT/US2015/021675 filed on Mar. 20, 2015,which in turn claims the benefit under 35 U.S.C. § 119(e) of ProvisionalApplication Ser. No. 61/968,453 filed on Mar. 21, 2014 entitled TRANSFILTER and all of whose entire disclosures are incorporated by referenceherein.

BACKGROUND OF THE INVENTION

The present invention relates generally to devices that recover, detector demodulate signals, and more particularly, to devices that providergreater sensitivity and noise rejection for the detection of FM Dopplerradar, geological or oceanographic sonar returns and for spread spectrumcommunication or hybrid envelope/exponent modulation systems.

Conventional FM detectors/demodulators suffer from a thresholdphenomenon which limits detection sensitivity of exponentially modulatedsignals (also referred to as “angle modulated signals”). Thesedetectors/demodulators typically utilize diode rectifiers and matchedfilters to recover the baseband information signals. However, suchdevices introduce non-linearities, e.g., noise cross products, that arethe root cause of the threshold phenomenon.

As predicted by Claude Shannon, an FM demodulator is 1.77 dB moresensitive than a matched filter of equal bandwidth. Under this paradigm,the best that can be achieved by using the matched filter is an outputsignal-to-noise ratio (SNR) that is equal to the input carrier-to-noiseratio (CNR).

In particular, the current state-of-the-art in analog demodulators ordetectors of exponentially modulated signals can be categorized intoseveral broad classes. The first major class distinction considers thetreatment of additive white Gaussian noise (AWGN). There are methodsthat convert or transform stationary AWGN to a parabolic noise densitydistribution and those that do not. Those that do convert AWGN to aparabolic distribution all have a CNR threshold limitation below whichthe conversion ceases. Foster-Seely, Travis and Ratio Detector types ofexponential modulation demodulators, detectors or discriminators are theprimary types that perform the conversion when operating at (C/KT) abovethe threshold limitation. See FIGS. 1A and 1B which depict a Travis FMdiscriminator and a Foster-Seeley discriminator, respectively.

Another general class of exponential modulation detectors utilize someform of product detection. This class of detectors do not convert AWGNto a parabolic noise power distribution. At best, they do not degradethe output detected signal-to-noise-ratio to a value worse than theinput (CNR) or (C/KTB) where the input and output bands are equal. Amongthis type of detector are the Phase Locked Loop, the correlationdetector. The Phase Locked Loop uses a voltage controlled oscillator(VCO) to provide a replica of the received signal. The phase errorbetween the received signal and the VCO provides the signal that drivesthe VCO. It can have a threshold that is about 3 dB better that of theFoster-Seeley or Travis Demodulator. Other types of exponentialmodulation detectors are:

-   -   1. Pulse Counting Discriminator. This method uses a monostable        multivibrator or other pulse generator that produces a pulse of        constant amplitude and width each time the composite noise and        signal voltage crosses a reference value. The output pulses are        low pass filtered to reject the pulse repetition rate.        Fluctuation of the average value of the LP Filter output is the        baseband information. This type of demodulator has a high        threshold and is seldom used.    -   2. The FMFB utilizes negative feed-back to compress the received        spectrum prior to demodulation. This technique is effective for        small information bandwidths and has been used to carry up to        600 telephone channels on a single FDMFM carrier. The threshold        improvement is of the order of 3 dB.    -   3. I/Q Demodulators. This class of demodulator requires a high        degree of synchronization with the transmitted signal. The        received signal is broken down into In Phase and Quadrature        components. The multipliers or mixers used to perform the        conversion do not transform flat input noise density to        parabolic and so are limited to matched filter performance.        However, there is no threshold if the band can be made small        enough. Using this type of detector with a 1 Hz bandwidth the        signal and noise can be sampled and stored. Multiple samples can        be processed to effectively decrease the bandwidth and increase        (SNR). This technique is used to detect weak Doppler RADAR        returns.

Therefore, in view of the foregoing, all of these conventionaldemodulators fail to address the CNR threshold and, as a result, at orbelow this threshold the output signal is pure noise. Furthermore,because these configurations are demodulators, they do not operate asfilters and consequently these demodulators cannot be cascaded.

Thus, there remains a need to overcome this threshold phenomenon byusing filtering techniques which permit the cascading of stages thereof,that improves the SNR and which eliminates the need to utilize complextechniques to result in improved performance and design simplification.

All references cited herein are incorporated herein by reference intheir entireties.

BRIEF SUMMARY OF THE INVENTION

A filter that demodulates an exponentially modulated signal andcompresses noise in its signal band is disclosed. The filter comprises:a first frequency selective network using only linear components andwhich forms a frequency domain derivative operator that generates anoutput that is a function of a rate of change of a carrier frequency ofthe exponentially modulated signal at an input to said filter, whereinthe linear components minimize a threshold (e.g., CNR threshold) that isnormally present in exponentially modulated signal demodulators; andwherein the first frequency selective network is operative on anymodulation format of the exponentially modulated signal and generatesimpulses for abrupt changes in the carrier frequency corresponding todata transitions that form the baseband of the exponentially modulatedsignal while compressing noise in the signal band.

An additional embodiment comprises having a cascade of more than one ofthese filters that further compresses the signal band noise whileincreasing the amplitude of the impulses.

A method for demodulating an exponentially modulated signal andcompressing noise in its signal band is disclosed. The method comprises:feeding the exponentially modulated signal into a first frequencyselective network that uses only linear components for minimizing athreshold (e.g., CNR threshold) that is normally present inexponentially modulated signal demodulators; obtaining a frequencydomain derivative of the exponentially modulated signal that generatesan output which is a function of a rate of change of a carrier frequencyof the exponentially modulated signal, independent of a modulationformat used in the exponentially modulated signal; generating impulsesfor abrupt changes in the carrier frequency corresponding to datatransitions that form the baseband of the exponentially modulatedsignal; and compressing noise in the signal band.

An additional step comprises cascading more than one of these filterstogether to further compress the in-band noise while increasing theamplitude of the impulses.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

Many aspects of the present disclosure can be better understood withreference to the following drawings. The components in the drawings arenot necessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1A is a prior art demodulator, viz., Travis FM discriminator alongwith its frequency and signal characteristics, that operates above theCNR threshold;

FIG. 1B is another example of a prior art demodulator, viz.,Foster-Seeley discriminator along with its frequency and signalcharacteristics, that operates above the CNR threshold;

FIG. 2 is a block diagram of the filter invention of the presentapplication, hereinafter referred to as the “trans-filter” and alsodepicting a plurality of these trans-filters being cascaded forincreasing noise compression and impulse amplitude where these impulsesare generated at data transitions for many modulation formats;

FIG. 3 are respective frequency responses for the signal emanating fromthe upper frequency selective network, the lower frequency selectivenetwork and the signal emanating from the summer;

FIG. 4 depicts an exemplary analog version of the trans-filter using twolow pass filters in the upper path and two high pass filters in thelower path, where R2 and R4 are both parts of the low pass and high passfilters and the summing network;

FIG. 5 is another analog version of the trans-filter using two high passfilters and two low pass filters whose 180 degrees-out-phase outputs arethen fed to a summer and wherein the summer output, in certaincircumstances, may be processed to extract the baseband information;

FIG. 6 is the amplitude vs. frequency response of the two high and lowpass filters' outputs;

FIG. 7 is a vector diagram showing the amplitude and phase of v1 and v2vectors at the frequencies F₁, F₀ and F₂ of the trans-filtercorresponding to FIGS. 5-6;

FIG. 8 is a depiction of the carrier envelope at the sum output of thetrans-filter;

FIG. 9 is timewise depiction of the output multiplier;

FIG. 10 is a frequency diagram of input and output spectra of thetrans-filter, showing the output of the trans-filter having a null atthe center frequency even when no carrier, but only noise, is presentand demonstrating proof of the linearity (absence the threshold);

FIG. 11 is a diagram depicting the frequency spectrum at the outputs oftwo (by way of example only) cascaded trans-filters, showing the absenceof the threshold;

FIG. 12 is a block diagram of a test set up for evaluating a cascade offour (by way of example only) trans-filters and to which the followingFIGS. 13-23 pertain;

FIG. 13 depicts the frequency-shift keying (FSK) input signal that ishigh-pass-filtered and applied to a first trans-filter and wherein thesignal is at a level of −60 dBm at node ND4;

FIG. 14 depicts the trans-filter impulse output for the input signal ofFIG. 13 in accordance with the mark/space transitions at node ND15 at aninput (C/KT=−50 dB-Hz);

FIG. 15 is a spectrum diagram showing the input noise from the filter F0and the output of each trans-filter;

FIG. 16 is a voltage versus time measurement at the first trans-filterinput and wherein the vertical scale is ±200 volts and the quantityC/KT=−60 dB-Hz at node ND4;

FIG. 17 is a voltage versus time measurement at the second trans-filterinput and wherein the vertical scale is ±200 volts and the quantityC/KT=−60 dB-Hz at node ND5;

FIG. 18 is a voltage versus time measurement at the third trans-filterinput and wherein the vertical scale is ±200 volts and the quantityC/KT=−60 dB-Hz at node ND6;

FIG. 19 is a voltage versus time measurement at the fourth trans-filterinput and wherein the vertical scale is ±200 volts and the quantityC/KT=−60 dB-Hz at node ND9;

FIG. 20 is a voltage versus time measurement at the output of the firsttrans-filter, measured at node ND15, using a filter bank to reduce noiseat baseband and wherein the impulses and noise at the quantity C/KT=−50dB-Hz;

FIG. 21 is a voltage versus time measurement at the output of the secondtrans-filter, measured at node ND15, using a filter bank to reduce noiseat baseband and wherein the impulses and noise at the quantity C/KT=−50dB-Hz;

FIG. 22 is a voltage versus time measurement at the output of the thirdtrans-filter, measured at node ND15, using a filter bank to reduce noiseat baseband and wherein the impulses and noise at the quantity C/KT=−50dB-Hz;

FIG. 23 is a voltage versus time measurement at the output of the fourthtrans-filter, measured at node ND15, using a filter bank to reduce noiseat baseband and wherein the impulses and noise at the quantity C/KT=−50dB-Hz;

FIG. 24 is a block diagram of a digital trans-filter configuration ofthe present invention;

FIG. 25A is a low pass filter pole-zero z-plane representation of thelow pass arm of FIG. 24;

FIG. 25B is a high pass filter pole-zero z-plane representation of thehigh pass arm of FIG. 24;

FIG. 26 is the spectral response of the digital trans-filter;

FIG. 27 is the phase response of the digital trans-filter;

FIG. 28A-28B are the input signal and the input noise, respectively, tothe digital trans-filter;

FIG. 29A-29B are output signal and the output noise, respectively of thedigital trans-filter; and

FIG. 30 is a block diagram showing a plurality of digital trans-filtersbeing cascaded, including the use of the first embodiment of thetrans-filter being used as a noise compressor before the input signal isconverted to a digital signal.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the figures, wherein like reference numerals representlike parts throughout the several views, exemplary embodiments of thepresent disclosure will be described in detail. Throughout thisdescription, various components may be identified having specificvalues, these values are provided as exemplary embodiments and shouldnot be limiting of various concepts of the present invention as manycomparable sizes and/or values may be implemented.

The trans-filter 20 minimizes in-band noise and maximizes detectionsensitivity of exponentially-modulated signals 20 by eliminating thethreshold phenomenon that limits detection sensitivity of exponentiallymodulated signals (also referred to as “angle modulated signals”). Itaccomplishes this by elimination of nonlinear circuit elements (e.g.,diodes, transistors, non-linear magnetics, etc.) used in conventionalexponential modulation detectors such as phase or frequencydiscriminators.

The filter 20 is a linear circuit that detects or demodulates a varietyof different modulation formats. It differentiates the input signal andtransforms in-band stationary AWGN to a parabolic noise densitydistribution. The outputs of two parallel frequency selective circuitswith opposite amplitude slopes are subtracted. Stationary noisecomponents above and below the center frequency cancel each other,resulting in the parabolic noise density. The magnitude of the transferfunction is a “V-shaped” slope across the bandwidth of the filterreaching zero as the center frequency. The phase of the transferfunction abruptly changes by 180° at the center frequency. Rapidamplitude, phase or frequency variations in the input signal generateimpulses at the trans-filter 20 output. Differentiation of the inputsignal separates the baseband spectrum from the RF (radio frequency) orcarrier portion of the signal. The baseband, carrier and noise spectrallines all appear at the output in their respective bands. Since all ofthe components that comprise the trans-filter 20 are linear, there is nomultiplicative reaction between any of the spectral lines. This is thereason that there is no threshold associated with the trans-filter 20.Since the frequency spectra of the baseband, carrier and noise all existat the output of the trans-filter, but in their respective bands, theycan be separated by judicious filtering. Because flat noise at the inputis transformed by the linear slope into a parabolic noise densitydistribution and the power of a FM signal increases as the square of thedeviation, the output SNR is increased by the well-known FM improvementequation:Output SNR in f _(m) =P _(S) /P _(N)=(3/2)(C/KTf _(m))(ΔF/f_(m))²  (Equation #1)where:

-   P_(S)=signal power and P_(N)=noise power;-   C=input carrier signal power;-   K=Boltzman's Constant;-   T=Noise temperature in degrees K;-   f_(m)=highest frequency in modulated signal;-   ΔF=frequency deviation.    Equation #1 can be rewritten as:    Output SNR=(3/2)(C/KTB)(ΔF/B)²=(3/2)(CNR)(ΔF/B)²  (Equation #2)    where (C/KTB)=input (CNR) in the information band B. The    trans-filter 20 provides FM improvement without the threshold    limitation of conventional FM demodulators. This results in a more    sensitive radio wave detector that can operate in noisier    environments and with much weaker signals than any other    currently-used devices. The sensitivity of this device is greater    than that of the “matched filter” by the factor (3/2)(ΔF/B)², known    in the industry as the “FM Improvement Factor.”

In contrast, the quantity C/KTB is also the optimum SNR or the best thatcan be achieved with a matched filter. Thus, in conventionaldevices/methods, the best performance is given by:Output SNR_(matched filter)=Input CNR.

As will also be discussed below, a plurality of identical trans-filters20 can be cascaded, with each one providing additional rejection ofin-band noise while passing exponentially-modulated signalsundiminished. For FSK (frequency-shift keying), BPSK (binary phase shiftkeying) and PAM (pulse amplitude modulation) and other exponentiallymodulated signals, cascading trans-filters produces increasingly largeimpulses at the signal transitions. The fundamental frequency of thetransients occur at baseband and can be recovered without additionalfrequency conversion or synchronization. In addition, the transients,having a large peak to average ratio, are even more easily detected.Doppler and data rate information may also be obtained from theimpulses, thereby simplifying the demodulation process.

The trans-filter 20 may be used to provide superior reception in amultitude of applications such as digital FM broadcast of voice ormusic, digital data, GPS, radar, sonar, medical imaging, geographicalmapping, and oil/mineral exploration, by way of example only.

The trans-filter 20 accomplishes this by using linear frequency or phasesensitive networks that produce outputs that maintain a 180 degree phaserelationship relative to each other over the exponential modulationband. The frequency sensitive network outputs can then be summed toproduce an output whose amplitude is proportional to frequency or phasedeviation of the input signal. Hybrid signal modulation methodsutilizing both amplitude modulation (AM) and phase modulation (PM) canalso benefit from the noise rejection characteristics of thetrans-filter 20.

It should be noted that the term “filter” as used with regard to thetrans-filter 20 is meant by Applicant to describe any implementation ofthe features associated with the trans-filter 20. Therefore, the term“filter” is not limited to a discrete component design or even an analogdesign but also includes a solid state/integrated circuit configuration,a digital implementation formed in computer code, or any other manner ofimplementing the features of the trans-filter 20 as described herein. Inaddition, the trans-filter 20 can be a module, or a stage(s) in a largerapparatus or device such as, but not limited to, a data or communicationreceiver, etc. Furthermore, the term “filter” is meant to cover one ormore of the trans-filters 20 if a cascade (e.g., at least twotrans-filters 20 are coupled together) of these trans-filters 20 isimplemented.

In particular, as shown in FIG. 2, a frequency modulated (FM) signal I,including additive white Gaussian noise (AWGN), is fed into an input 22to the trans-filter 20. The signal I is simultaneously fed to afrequency selective network 24A that is tuned above the center frequency(e.g., two single high pass filters, or an even number thereof) and afrequency selective network 24B that is tuned below the center frequency(e.g., two single pole low pass filters, or an even number thereof),both of which are linear, to generate respective slope-weighted signals26A and 26B that are 180° out of phase. Network 24A shifts the phase ofFM signal 10 by +90° while network 24B shifts the phase of FM signal 10by −90°. As the input frequency varies (over F₀+ΔF), the signals 26A and26B (having respective vector notations, v1 and v2) remain at 180° phaserelative to each other. Thus, at the center frequency (F₀), the signals26A and 26B are equal in amplitude and 180° out of phase. See FIGS. 3and 6-7. These two signals 26A and 26B are then fed to a summing network27 (also linear), thereby output signal 28 having a zero amplitude atthis frequency, F₀. This accounts for the linear rejection of stationarynoise density voltage that results in parabolic weighting of noise powerdensity over the baseband. The signal deviation is undiminished andtherefore the trans-filter 20 reduces only the stationary AWGN.

As mentioned previously, the outputs 26A/26B of the two frequencysensitive networks are summed together at the sum network 27 to producea single output 28. The sum output 28 has the same instantaneousfrequency as the input. The instantaneous amplitude is a function of thefrequency offset from the center frequency. The carrier phase at thesummer output 28 reverses each time the carrier passes through thecenter frequency. This gives the output 28 the appearance of a DoubleSideband Suppressed Carrier (DSBSC)-like waveform with a frequencymodulated carrier inside the envelope. The carrier phase at the sum 28output is shown in FIG. 7 for a single tone analog FM carrier input.

FIGS. 4 and 5 provide two exemplary analog embodiments, namely, 20A and20B, respectively, of the trans-filter 20 and as described previously,because the noise is compressed, the edges of the modulated signal canbe easily identified. As a result, there is no need for any conventionaldemodulation. However, in some circumstances (e.g., in a detector for aDoppler radar, also referred to as a “correlation receiver) the basebandsignal may be recovered by using a conventional demodulation stage 10,as shown in FIG. 5; in particular, the demodulation stage 10 multipliesthe sum output 28 by a noiseless synchronized replica 12 of thetransmitted signal. Furthermore, the multiplier 14 (e.g., productdetector) is linear and produces only the sum and difference products ofthe inputs (see FIG. 9). A low pass filter 16 ejects the carrier and thehigh order product.

As can be seen from FIGS. 4-5, the frequency selective network tunedabove the center frequency 24A may comprise two high pass filters,HP1/HP2 while the frequency selective network tuned below the centerfrequency 24B may comprise two low pass filter LP1/LP2. The respectiveoutput of these two networks are the signals 26A/26B, discussedpreviously.

It should be further noted that the linear frequency selective networks24A/24B may each comprise respective bandpass filters.

As mentioned earlier with regard to the vector diagrams (FIG. 7), theoutput spectrum of the trans-filter 20 has a null at the centerfrequency, F₀, even when no signal is present. See FIG. 10 where M(3)depicts the input noise spectrum and M(6) depicts the output noisespectrum of a single trans-filter with no signal present. Cascadingidentical trans-filters 20, as shown in FIG. 2, results in increasednoise rejection multiplicatively. The limit is the intrinsic noise ofthe filter and summing network 27 elements used. Signal transmissionthrough multiple trans-filters 20 is also multiplicative. The resultingdistortion can be compensated for by pre-distortion in a fashion similarto pre-emphasis of audio signals in FM Broadcasting. See FIG. 11 whichillustrates the additional noise suppression provided by cascading two(by way of example only) trans-filters 20. Thus, a key improvementprovided by the trans-filter 20 is cumulative, i.e., cascadingtrans-filters 20 of equal bandwidth results in increased improvement ofsignal-to-noise (SNR) ratio. As a result, if one trans-filter 20provides 20 dB improvement in the SNR, then two identical trans-filters20 provide 40 dB improvement in SNR. In contrast, cascading “matchedfilters,” of equal bandwidth, produces no additional improvements inSNR.

Cascading trans-filters 20 increases noise rejection, thus increasingthe SNR even more relative to a matched filter approach. This can beperformed at different intermediate frequencies to avoid having too muchgain at any one frequency.

It should be understood that any linear networks having the propertiesof 180 degree-relative output phase and linear amplitude variation overthe FM band under consideration would allow the cited performance to beachieved. Furthermore, it should be understood that analogrepresentations of the trans-filter 20 of FIGS. 4-5 are provided by wayof example only and that digital numeric implementations (also referredto as an “algorithmic representation”) of the trans-filter 20 are withinthe broadest scope of the present invention to provide ideal performancewith perfect stability. The digital numeric implementation oralgorithmic representation is used to detect or demodulate exponentiallymodulated signals that have been converted to the digital domain byanalog-to-digital converter (ADC).

The trans-filter 20 discriminates against stationary AWGN in the signalband (See FIG. 10), thereby increasing the CNR prior to detection.Unlike any conventional band pass filter (e.g., a (matched filter), aplurality of trans-filters 20 of equal bandwidth can be cascaded,providing additional rejection of stationary AWGN in the pass band (SeeFIG. 11). The term “signal band” or “in-band” refers to the bandoccupied by the transmitted signal.

Thus, the foregoing discloses an apparatus and method that eliminatesthe threshold phenomenon that limits detection sensitivity ofexponentially modulated signals. The apparatus and method achieve thisby the elimination of nonlinear components and modification of thefrequency selective networks to produce a sloping amplitude that isproportional to frequency offset from a center frequency and passesthrough zero at the center frequency. The opposite sloping amplitude and180 degree phase difference cause the noise cancellation that transformsflat AWGN to a parabolic shape. The amplitude slope with frequency andthe rapid phase reversal at the crossover frequency produce largepolarized impulses at the transitions for digitally modulated signals ofall types, thereby making the trans-filter 20 a universal demodulator.Elimination of non-linear circuit elements, compression of in-band noiseand the derivative action of the sloping amplitude vs. frequencycharacteristic together with the abrupt phase reversal at crossover,combine to produce large polarized impulses at the modulation rate(Baseband) and do not require conversion to baseband. Cascadingtrans-filters 20 increases the magnitude of the impulse relative to thenoise and carrier leakage.

Trans-Filter 20 Impulse Generator/Demodulator

The trans-filter 20 transfer function is basically a frequency domainderivative operator. It generates an output that is a function of therate of change of the frequency at its input. As a result, thetrans-filter 20 generates impulses when the input frequency changesabruptly. This is true for all types of digital modulation, whether itbe phase, frequency or even abrupt changes of amplitude such as PAM.

The instantaneous reversal of phase of the transfer function when thesignal crosses the center frequency of the trans-filter 20 producespolarized impulses that are proportional to the instantaneous frequencychange, df/dt, and its sign. For a PAM signal at the trans-filter 20center frequency, the change in going from off to on is +F_(o). At theend of the pulse the change is −F_(o). Either of these changes generatea large enough instantaneous frequency to produce the maximum + or −output of the trans-filter 20. For FSK signals, the output of the firsttrans-filter 20 is more a sine/cosine conversion rather than an impulse.The second and subsequent trans-filters 20 do produce increasingly largeimpulses both due to the phase reversal at center frequency and thesharpness of the transition due to the higher order derivative.

While the impulses are generated at the trans-filter output 28 that iscentered on F_(o), their fundamental frequency (viz., the data rate) isat baseband. The trans-filter 20, due to its derivative characteristic,demodulates (viz., converts to baseband) the received signal. Sincethere are no non-linear components in the trans-filter 20, there is nointeraction between any of the frequency components, be they signal ornoise. Thus, as discussed previously, there is no threshold phenomenon.

The slope of the trans-filter 20 transfer function converts stationarynoise power to a parabolic shape which when integrated over thetransmission band relative to the modulation band yields an improvementof [10 log(3/2)+20 log(ΔF/B)] for a single unit due to noise reductiononly. For two trans-filters 20, the noise reduction improvement is [10log(5/2)+40 log(ΔF/B)]. For N identical trans-filters 20 cascaded, thereduction in noise is [10 log((2N+1)/2)+20N log(ΔF/B)]. The increase insignal impulse voltage with each additional stage is more difficult toevaluate since it is highly dependent the form of modulation and uponrise time limitations. The data in FIGS. 20-23 for 4 cascaded stageswith a PAM input indicates an increase of approximately 3 dB in signalamplitude for each added stage.

FIG. 12 depicts a block diagram of a test setup 100 used to evaluate theresponse of a cascade of four (by way of example only) identicaltrans-filters 20. An FSK signal is generated using two oscillators and aswitch. The mark and space frequencies are C1 at 105 KHz and C2 at 95KHz. Switching rate is 50 Hz determined by Pulse Generator S1. Noise isprovided by noise generator N. Total noise output power is 0 dBm in a 1MHz band that is uniform in density at −60 dBm/Hz. Signal power at inputto summer A1 is 0 dBm. FIGS. 13-23 depict the signals and signalresponses of this test setup 100. It should be noted that with regard tothe test setup 100, the following information is pertinent:

-   Carrier Power=C=0 dBM-   for FSK modulation FCN=2;-   Noise Power Density=−164 dBm/Hz;-   For T=3,000 Deg Kelvin;-   (C/KT)=−48 dB-Hz for Ps=−212 dBm;-   Simulation step size=5E-7 sec; and-   Simulation time=0.11 sec.

Noise and signal are combined by the summing network A1. The values ofG1 and G2 are used to establish the (C/KT) ratio for each measurement.The value of G1 establishes noise and ranges from 0 to 1E3 (whichcorresponds to 10³). G2 ranges from 0 to 1E-3 (which corresponds to10⁻³). RMS power meters M1 and M2 are provided to measure signal andnoise powers to establish the (C/KT) operating point for themeasurements. A high pass filter F0 is used to attenuate any vestiges ofthe baseband signal to a negligible value.

FIG. 13 shows the FSK signal of the filter F0 output which is fed to thefirst trans-filter 20; the signal at this point is at a level of −60dBm. FIG. 14 shows the output pulse resulting from the mark/spacetransition with respect to FIG. 13. FIG. 15 is a spectrum diagramshowing the input noise from the filter F0 and the output of eachtrans-filter 20 (TF1, TF2, TF3 and T4 shown in FIG. 12). Thetrans-filter TF1/TF2/TF3/TF4 outputs do not appear parabolic because thevertical scale in FIG. 15 is logarithmic; however, as discussedpreviously, each trans-filter 20 operates to transform flat noise by thelinear slope relationship into a parabolic noise density distribution.

A series of high pass, low pass and band reject filters are provided atthe output of the cascaded trans-filters 20 to attenuate noise thattends to obscure the impulses generated by the mark/space transitions.That same chain of filters is used to view the output of eachtrans-filter 20 (namely, TF1, TF2, TF3 and TF4) in the test circuit 100at node ND15; thus, the views of FIGS. 20-23 depict the output oftrans-filters TF1, TF2, TF3 and TF4, respectively. The band rejectfilters contribute negligible attenuation and degradation to theimpulses that emanate from the summer A1.

FIGS. 16-19 clearly depict the successive compression of the noise atthe output of TF1 (node ND4), TF2 (node ND5), TF3 (node ND6) and TF4(node ND9). FIGS. 19-22 clearly depict the successive accentuation ofthe impulse outputs of each trans-filter TF1-TF4 as they are viewed atnode ND15.

FIGS. 24-30 are directed to a digital version of the trans-filter,hereinafter referred to as the digital trans-filter (DTF) 120. Inparticular, FIG. 24 is a block diagram of the DTF 120. The DTF 120 is alattice filter in which one arm performs a monotonic low pass filterfunction, while a second arm performs a monotonic high pass filterfunction. These filters are designed so that cascading two filters ineach arm results in a 180 degree phase shift between the two arms; assuch, the amplitude responses of the two arms are exactly equal at thecenter of the band, i.e., at the sampling frequency (F_(S)) divided byfour, F_(S)/4 or also referred to as half of the Nyquist Frequency.

FIGS. 25A/25B provide the low pass filter pole-zero z-planerepresentation of the low pass arm and the high pass filter pole-zeroz-plan representation of the high pass arm, respectively.

When the output of the two arms are added together at the summingnetwork 127 of the DTF 120, the noise completely cancels at the centerof the band and is reduced throughout the band; however, the signaldeviation remains the same, resulting in increased SNR. The DTF's 120spectral response is shown in FIG. 26. FIG. 27 is the phase response ofthe DTF 120. FIGS. 28A-28B depict the signal input and the noise input,respectively, to the DTF 120. FIGS. 29A-29B depict the signal output andthe noise output, respectively at the DTF 120. In particular, FIGS.28A-29A depict separate processing of noise and an FSK signal with arandom bitstream message and carrier frequencies 0.2 and 0.3 timesF_(S). For best performance, these are arranged symmetrically around thetrans-filter 120 null. Since the trans-filter 120 is completely linear,it is valid to look at the noise and signal components separately. Itcan be seen that the noise level is reduced. The signal is seen to bedemodulated, where each transition in the carrier frequency results inan impulse, positive for a transition from lower to higher frequency,and negative for a transition from higher to lower frequency. Aspreviously described, the trans-filter 120 converts wideband exponentialsignals, in this case (by way of example only), FSK, into a set ofpositive and negative impulses. An output filter is used after thetrans-filters 120 to remove non-impulsive energy. Since impulses have awhite spectrum, this involves removing all narrowband energy prior toidentifying the positive and negative impulses. This filtering stepincreases output SNR and removes the FM carrier frequency orfrequencies.

As with the trans-filter 20, the DTF 120 can be cascaded with other DTFs120 to increase noise compression and enhance impulse amplitudes fordetection of the exponentially modulated signal.

It should be further understood that the trans-filter 20 may also act asa pre-stage for an analog-to-digital (A/D) converter in a reconfigurablereceiver to compress the noise in the analog input signal prior to theA/D conversion process. For example, as also shown in FIG. 30, thetrans-filter 20 can compress in-band noise before the analog signal isdigitized (e.g., an A/D converter). The digitized signal is theninputted into a cascade of DTFs 120. In particular, the trans-filter 20may be used in cases where the SNR would be adversely affected by thedigitizer's quantizing noise. After digitization, one or more DTFs allowdetection at improved SNR. It should be further noted that the first DTF120 in the cascade detects the signal, whether analog or digital. Asdiscussed previously also, in some circumstances the output signal ofthe final DTF 120 of the cascade can be further filtered (e.g., the lowpass filter 16 as shown in FIG. 5).

In view of the foregoing, the key features of the trans-filter 20/120for digitally-modulated signals are:

(1) compresses noise in the signal band;

(2) generates impulses at data transitions for any modulation format;

(3) can be cascaded with other trans-filters 20/120 to increase noisecompression and impulse amplitude;

(4) demodulates carrier regenerating transitions of data stream;

(5) experiences a latency equal to one bit period; and

(6) requires no precision oscillators or timing.

While the invention has been described in detail and with reference tospecific examples thereof, it will be apparent to one skilled in the artthat various changes and modifications can be made therein withoutdeparting from the spirit and scope thereof.

What is claimed is:
 1. A filter that demodulates an exponentiallymodulated signal and compresses noise in its signal band, said filtercomprising: a first frequency selective network and a second frequencyselective network using only linear components and which form afrequency domain derivative operator that generate an output that is afunction of a rate of change of a carrier frequency of the exponentiallymodulated signal at an input to said filter, said linear componentsminimizing a threshold that is normally present in exponentiallymodulated signal demodulators; said first frequency selective networktuned above a center frequency of the exponentially modulated signal andsaid second frequency selective network tuned below the center frequencyof the exponentially modulated signal, said first frequency selectivenetwork and said second frequency selective network being configured inparallel and both receiving the exponentially modulated signal as afirst input signal, said first frequency selective network generating afirst output signal and said second frequency selective networkgenerating a second output signal, and wherein said first output signaland said second output signal are 180 degrees out of phase; and asumming network for receiving said first and second output signals andsumming said first and second output signals to generate impulses forabrupt changes in the carrier frequency corresponding to datatransitions that form the baseband of said exponentially modulatedsignal; and wherein said filter is operative on any modulation format ofsaid exponentially modulated signal and generates said impulses whilecompressing noise in the signal band.
 2. The filter of claim 1 wherein aphase of said first output signal comprises +90 degrees and a phase ofsaid second output signal comprises −90 degrees.
 3. A method fordemodulating an exponentially modulated signal and compressing noise inits signal band, said method comprising: feeding the exponentiallymodulated signal into a filter comprising first and second frequencyselective networks that use only linear components for minimizing athreshold that is normally present in exponentially modulated signaldemodulators, said first frequency selective network being tuned above acenter frequency of the exponentially modulated signal and said secondfrequency selective network being tuned below the center frequency ofthe exponentially modulated signal, said first frequency selectivenetwork and said second frequency selective network being configured inparallel and both receiving the exponentially modulated signal as afirst input signal, said first frequency selective network generating afirst output signal and said second frequency selective networkgenerating a second output signal, and wherein said first output signaland said second output signal are 180 degrees out of phase; summing saidfirst and second output signals to generate impulses for abrupt changesin the carrier frequency corresponding to data transitions that form thebaseband of said exponentially modulated signal, said impulsescorresponding to a frequency domain derivative of said exponentiallymodulated signal which is a function of a rate of change of the carrierfrequency of the exponentially modulated signal, independent of amodulation format used in said exponentially modulated signal; andcompressing noise in said signal band.
 4. The method of claim 3 furthercomprising the steps of: feeding said impulses into at least a secondfilter comprising a third frequency selective network and a fourthfrequency selective network both of which also use only linearcomponents for also minimizing a threshold that is normally present inexponentially modulated signal demodulators, said third frequencyselective network being tuned above the center frequency of theexponentially modulated signal and said fourth frequency selectivenetwork being tuned below the center frequency of the exponentiallymodulated signal, said third frequency selective network and said fourthfrequency selective network also being configured in parallel and eachgenerating third and fourth outputs, respectively, that are also 180degrees out of phase; and summing said third and fourth output signalsto generate a second derivative of said impulses while furthercompressing noise in the signal band and further increasing amplitudesof said impulses.
 5. The method of claim 3 wherein said step of feedingthe exponentially modulated signal into said filter comprises formingsaid first output to have a phase of +90 degrees while forming saidsecond output to have a phase of −90 degrees.
 6. The method of claim 4wherein said step of feeding said impulses into a second filtercomprises forming said third output to have a phase of +90 degrees whileforming said fourth output to have a phase of −90 degrees.
 7. A system,formed of at least two filters, that demodulates an exponentiallymodulated signal and compresses noise in its signal band, said systemcomprising: a first filter comprising: a first frequency selectivenetwork and a second frequency selective network using only linearcomponents and which form a frequency domain derivative operator thatgenerates an output that is a function of a rate of change of a carrierfrequency of the exponentially modulated signal at an input to saidfirst filter, said linear components minimizing a threshold that isnormally present in exponentially modulated signal demodulators; saidfirst frequency selective network tuned above a center frequency of theexponentially modulated signal and said second frequency selectivenetwork tuned below the center frequency of the exponentially modulatedsignal, said first frequency selective network and said second frequencyselective network being configured in parallel and both receiving theexponentially modulated signal as a first input signal, said firstfrequency selective network generating a first output signal and saidsecond frequency selective network generating a second output signal,and wherein said first output signal and said second output signal are180 degrees out of phase; and a first summing network for receiving saidfirst and second output signals and summing said first and second outputsignals to generate impulses for abrupt changes in the carrier frequencycorresponding to data transitions that form the baseband of saidexponentially modulated signal; and wherein said filter is operative onany modulation format of said exponentially modulated signal andgenerates said impulses while compressing noise in the signal band; anda second filter comprising: a third frequency selective network and afourth frequency selective network using only linear components andwhich also form a frequency domain derivative operator that receive saidimpulses from said first filter and obtains a second derivative of saidimpulses, said second filter further compressing noise in the signalband and further increasing amplitudes of said impulses; and said thirdfrequency selective network tuned above the center frequency of theexponentially modulated signal and said fourth frequency selectivenetwork tuned below the center frequency of the exponentially modulatedsignal, said third frequency selective network and said fourth frequencyselective network also being configured in parallel and each havingoutputs that are also 180 degrees out of phase and which are fed to asecond summing network for generating a second derivative of saidimpulses.
 8. The system of claim 7 wherein a phase of said first outputsignal comprises +90 degrees and wherein a phase of said second outputsignal comprises −90 degrees.
 9. The system of claim 7 wherein saidthird output signal comprises +90 degrees and wherein a phase of saidfourth output signal comprises −90 degrees.